How many solutions does this system have? {9x + 3y = 2 {y = -3x + 5/3 a) 1 solution b) 2 solutions c) no solutions  d) infinite solutions

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Solve the system:  `9x + 3y = 2`

                            `y = -3x + 5/3`

First, multiply 2nd equation by 3 nd rewrite in `ax + by =c`  form.

This gives us:  `3y = -9x + 5`

                      `-9x - 3y = -5`

Using the elimination method, add the 2 equations together.

`9x + 3y = 2`

`-9x-3y = -5`

`0 = -3`

Since `0!=-3,`

there is no solution.

Therefore, choice "c - no solutions"  is the correct solution.

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